A charged particle moving in a magnetic field experiences a resultant force

Options

A. In the direction opposite to the field
B. In the direction of field
C. In the direction perpendicular to both the field and its velocity
D. None of the above

Answer

To solve the question regarding the resultant force experienced by a charged particle moving in a magnetic field, we can follow these steps:

### Step 1: Understand the Magnetic Force Equation
The magnetic force \( F \) experienced by a charged particle moving in a magnetic field is given by the equation:
\[ F = q(\mathbf{V} \times \mathbf{B}) \]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( \mathbf{V} \) is the velocity vector of the particle,
- \( \mathbf{B} \) is the magnetic field vector.

### Step 2: Analyze the Cross Product
The term \( \mathbf{V} \times \mathbf{B} \) represents the cross product of the velocity and magnetic field vectors. The properties of the cross product indicate that the resultant vector is perpendicular to both \( \mathbf{V} \) and \( \mathbf{B} \).

### Step 3: Determine the Direction of the Force
Since the magnetic force is given by the cross product, the direction of the resultant force \( F \) will be perpendicular to the plane formed by the vectors \( \mathbf{V} \) and \( \mathbf{B} \). This means:
- The force is not in the direction of the magnetic field \( \mathbf{B} \).
- The force is also not in the direction of the velocity \( \mathbf{V} \).

### Step 4: Conclusion
Thus, the resultant force experienced by the charged particle moving in a magnetic field is perpendicular to both the velocity vector and the magnetic field vector. Therefore, the correct statement is that the resultant force is perpendicular to both the velocity and the magnetic field.

### Final Answer
The resultant force experienced by a charged particle moving in a magnetic field is **perpendicular to both the velocity vector and the magnetic field vector**.

---